Find the distance between $(-8,4)$ and $(-8,-2)$.
Answer (1)
Identify the coordinates of the two points: ( − 8 , 4 ) and ( − 8 , − 2 ) .
Apply the distance formula: d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .
Substitute the coordinates into the formula and simplify: d = (( − 8 ) − ( − 8 ) ) 2 + (( − 2 ) − ( 4 ) ) 2 = 0 + 36 = 36 .
Calculate the distance: 6 units.
Explanation
Problem Analysis We are given two points, ( − 8 , 4 ) and ( − 8 , − 2 ) , and we want to find the distance between them. We can use the distance formula to calculate this distance.
Distance Formula The distance formula is given by: d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the coordinates of the two points.
Applying the Formula Let's plug in the coordinates of our points into the distance formula: ( x 1 , y 1 ) = ( − 8 , 4 ) ( x 2 , y 2 ) = ( − 8 , − 2 ) d = (( − 8 ) − ( − 8 ) ) 2 + (( − 2 ) − ( 4 ) ) 2 d = ( 0 ) 2 + ( − 6 ) 2 d = 0 + 36 d = 36 d = 6
Final Answer The distance between the points ( − 8 , 4 ) and ( − 8 , − 2 ) is 6 units.
Examples
Imagine you're designing a video game and need to calculate the distance between two characters on a 2D map. If one character is at coordinates (-8, 4) and another is at (-8, -2), you can use the distance formula to find out how far apart they are. This helps in determining if they are within attacking range or if a character needs to move to reach the other. In this case, the characters are 6 units apart.
